The nipples are snapping? That seems odd, I have caused and witnessed plenty of wheel failures and have never seen a nipple break. By nipple, I assume you mean the part protruding from the rim that you can turn to apply tension to the spoke.
Typically the spokes themselves will break, either near the nipple or the spoke head by the hub.
Breaking nipples is not normal even for a big guy on a 32 spoke rim - I would regard the whole wheel as suspect and ask the shop to replace the wheel. If they wont replace it, at least check the tension on the spokes. With some patience you can make factory wheels stronger by evening tension, this can be done by ear with the wheel on the bike with a spoke wrench. A lot has been written on truing here and elsewhere on the web.
Sheldons' site is a good source for information, but I think some of his opinions are a bit dated. Bicycle and materials technology has advanced a lot since the 80's. 32 spokes is not a necessarily a weak wheel for a Clyde, but the wheel does have to be built right. 32 spokes are more than adequate to deal with loads placed on the wheel, the spokes will not fail due to overload. Cyclic fatigue kills the spokes over time, simply adding more spokes will not reduce this effect greatly. The wheel has to be built to minimize flexion and stress risers. I have a 28 spoke rear wheel which I have ridden hard for 4 seasons without any issues or truing. Another wheelset i use has 20 spokes on the rear and have not had any breakage over several thousand miles, but I do carry a spare spoke just in case.
I do ride a 36 rear 32 front combination on my "beater" road bike - I still get the occasional broken spoke on the rear. One advantage a 36 spoke wheel has is that the wheel is still pretty rideable if a spoke breaks.
My recommendation is to replace the wheel. If you get a factory wheel be sure to check the spoke tension. If you can upgrade for a handbuilt, go for it. Don't be surprised if the wheelbuilder recommends a 32 spoke over a 36 spoke wheel - it will still be stronger than what you have, and they will guarantee it.